I was never very good at the heat transfer thing.......picking / estimating / guess heat transfer coefficients was too much black art for me.
I've got ~30 to 40' of unisulated 3/4" (trade size) copper tube running through an unheated (but insulated) crawlspace.
Here's my question
Is it worth the savings to drag my 50 year old body through the access hole & put on some of the split tube foam insulation? Or is the savings high enough to justify paying to have it done?
Hot water temp ~120F but sometimes as high as 140F (temp boosted to compensate for very high shower usage) Crawlspace tmep ~45F Flow rate ~1gpm Daily hot water usage ~50 to 150 gallons
How many Btu's, per gallonn of water used, are being lost through the copper tubing?
I am going to pick numbers out of the air, just to get some kind of feel for the numbers involved.
I suppose that:
after last use of the day, the water will cool to ambient with or without a jacket.
after first use of the day, the delay til next use will determine the cooling of the pipe contents which will vary with the thermal impedance of the pipe. (1)
during use, the terminal temperature will be lower with uninsulated pipe than using sleeve. (2)
Loss estimates (1) uninsulated Time constant = 6 minutes insulated tc = 18 min (TC = time to fall to 37% of initial delta t )
(2) T input 140 f output 114F uninsulated, 134 F insulated.
Suppose interval between a shower end and next shower begin is 10 minutes Suppose power is 10cents per kWhr. Volume at risk: 40 ft X 12 in/ft X pi X 3/4 in / 4 = 283 cu in =
4633 cc Volume per day 120 gal
delta t = 140 - 45 = 95F
Uninsulated Energy loss (1) ====================== Temperature drop in 10 minutes no flow 95 X 0.63 = 60 F plus 35 X 2/3 X 0.63 = 15F - this gives 140 - 60 - 15 = 65F = 36C
Heat loss 36 C X 4633 cc X 4.2 joule/cal = 0.7 MJ
Number of showers at 15 min /shower = 120/15 = 8 Total standing loss uninsulated 7 X 0.7 MJ = 4.9 MJ per day
10 cents kWhr = 10 cents per 3.6 MJ
Cost/day of standing loss = 4.9/3.6 X 10 cents = 14 cents /day = $49.70 per year. Amortize over 10 years total cost $497
Insulated Energy Loss (1) ==================== Temp drop in 10 min no flow 95 X 0.63 X 10/18 = 38 F = 21C
Heat loss 21C X 4633 cc X 4.2 joule/cal = 0.4 MJ
Total standing loss insulated 7 X 0.4 MJ = 2.8 MJ per day
Cost/day of standing loss = 2.8/3.6 X 10 cents = 8 cents /day = $28.39 per year Over 10 years, total standing heat loss cost $284
Uninsulated Energy Loss (2) ======================
140 - 114F = 26F delta T X 120 gal/day = 14.5C X 120 gal/day X 8 lb/gal / 2.2 lb/kg X 1000 cc/kg X 4.2 joule/cal = 26.6MJ/day Cost per day of running water heat loss 26.6 / 3.6 X 10 cents = 74 cents/day = $270 /yr Over 10 years total running heat loss cost = $2700
Insulated Energy Lass (2) ====================
140 - 134 = 6F delta T X 120 gal/day = 3.3C X 120 gal/day X 8 lb/gal /2.2 lb/kg X 1000 cc/kg X 4.2 J/cal = 6.1 MJ/day Cost per day of running water heat loss 6.1 / 3.6 X 10 cents = 17 cents/day = $61.94 /yr Over 10 years total running water heat loss cost = $619
This sounds like an example of proper selection of the thermodynamic universe -
you said it was insulated - if the pipes are between the insulation and the floor, the heat lost from the pipe goes up into the living space. It is not lost to the dwelling. However, it may add to cooling load.
if it is insulated between the pipes and the floor - as in the joists - the heat is lost.
As to non-heat considerations - If the ambient can go near freezing because of venting, etc., or the copper is over bare damp acidic soil, or if you use the plumbing as a service ground and you don't have a secure fitting ground rod, you will need frost and galvanic protection.
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